Effective Flory interaction parameter and disparity in equation-of-state properties for block copolymers

Effect of Disparity in Self Dispersion Interactions on Phase Behaviors of Molten A-b-B Diblock Copolymers

Phase behaviors of molten A-b-B diblock copolymers with disparity in self dispersion interactions are revisited here. A free energy functional is obtained for the corresponding Gaussian copolymers under the influence of effective interactions originating in the localized excess equation of state. The Landau free energy expansion is then formulated as a series in powers of A and B density fluctuations up to 4th order. An alternative and equivalent Landau energy is also provided through the transformation of the order parameters to the fluctuations in block density difference and free volume fraction. The effective Flory χ is elicited from its quadratic term as the sum of the conventional enthalpic χH and the entropic χS that is related to energetic asymmetry mediated by copolymer bulk modulus. It is shown that the cubic term is balanced with Gaussian cubic vertex coefficients in corporation with energetics to yield a critical point at a composition rich in a component with stronger self interactions. The full phase diagrams with classical mesophases are given for the copolymers exhibiting ordering upon cooling and also for others revealing ordering reversely upon heating. These contrasting temperature responses, along with the skewness of phase boundaries, are discussed in relation to χH and χS. The pressure dependence of their ordering transitions is either barotropic or baroplastic; or anomalously exhibits anomalously both at different stages. These actions are all explained by the opposite responses of χH and χS to pressure.

Pressure Effects on Self-Assembly in Mixtures Containing Zwitterionic Amphiphiles

To understand the responses of self-assembly in mixtures containing zwitterionic amphiphilic chains to high pressure, we introduce a self-consistent field theory in combination with a molecular equation-of-state model for them in a primitive way. The free energy density for those in the bulk state is first formulated. Its locally equilibrated excess part is then incorporated into Edwards Hamiltonian along with the electrostatic energy contributions to elicit the saddle point approximation to the partition function with proper self-consistent field equations. It is shown that charge-charge correlations enhance self-assembling tendency for the amphiphiles with the opposite charges on one component side, as the medium dielectric constant ε_r decreases. Those with the opposite charges at the two chain ends respond in a more complicated way to ε_r. Densification by applied pressure strengthens the self-assembly for both at a moderate ε_r, similar to typical phospholipids, but pressure effects are strongly dependent on the position of charges along the chains at a lower ε_r. It is argued that the manipulation of the dielectric environment and disparity in component dispersion interactions can yield useful materials exhibiting various types of baroresponsivity or thermoresponsivity with re-entrant self-assembly.

Identification of Some New Triply Periodic Mesophases from Molten Block Copolymers

Using field-theoretic simulations based on a self-consistent field theory (SCFT) with or without finite compressibility, nanoscale mesophase formation in molten linear AB and ABC block copolymers is investigated in search of candidates for new and useful nanomaterials. At selected compositions and segregation strengths, the copolymers are shown to evolve into some new nanostructures with either unusual crystal symmetry or a peculiar morphology. There exists a holey layered morphology with Im3 symmetry, which lacks one mirror reflection compared with Im3m symmetry. Also, a peculiar cubic bicontinuous morphology, whose channels are connected with tetrapod units, is found to have Pn3m symmetry. It is shown that there is another network morphology with tripod connections, which reveals P432 symmetry. The optimized free energies of these new mesophases and their relative stability are discussed in comparison with those of double gyroids and double diamonds.

Superposition in Flory-Huggins χ and Interfacial Tension for Compressible Polymer Blends

We investigate theoretically the response of interfacial tension γ for compressible polymer blends to thermodynamic variables. Helfand's self-consistent field theory is first extended to be combined with an off-lattice equation-of-state model to describe compressibility. Typical incompatible blends reveal that the effects of temperature and pressure (T-P) on γ are superposed into a single curve by a dimensionless pressure variable through the superposition in Flory-Huggins χ and density. In the case of polymer blends with strong compressibility difference, γ shows an anomaly upon pressurization with no T-P superposition, even though χ still follows the superposition.